The effect of aviation emissions on human-induced climate change has become a major concern in the last decades. The reduction of emissions, such as CO2 and NOx, is an important matter because of the predicted increase of the aviation market in the future years. The application of alternative fuels, such as hydrogen, and new combustion methods (e.g. lean premixed) are two of the main trends in order to reduce civil aviation emissions. The AHEAD (Advanced Hybrid Engines for Aircraft Development) project presented a novel hybrid engine concept. The proposed innovative design uses two combustion chambers. The first is a cryogenic fuel combustor, conceived to operate with liquid hydrogen or liquid natural gas, followed by an inter-turbine flameless biofuel combustor. In the present thesis, the lean premixed hydrogen combustor designed in the AHEAD project was simulated by applying a Computational Fluid Dynamics (CFD) method. The main objective of the present study is to find a set of CFD models which better characterize the named combustor, using exclusively the RANS (Reynolds Averaged Navier-Stokes) approach. Both a reactive and non-reactive approaches were followed. The results obtained were analysed and compared with experimental data. The RANS k-ε realizable turbulence model provided satisfactory qualitative results for the non-reactive case. The model predicted the characteristic features of the flow field obtained at swirling premixed combustors, such as the central and outer recirculation zones, the vortex breackdown, etc. The reactive flow field was not well characterized by the selected combustion models (e.g. Flamelet-Generated Manifold, Eddy Dissipation Concept). The main problem was found to be the mixing pattern predicted by the set of models used in the study. The RANS turbulence models applied were not accurate enough to obtain a satisfactory hydrogen-air distribution at the mixing area of the combustor. Further analysis is advised, adding a more detailed CFD approach such as the Large Eddy Simulation.